Doug C. answered • 11/03/23
Math Tutor with Reputation to make difficult concepts understandable
One way to do this:
Let n = 35.1515...
Multiply by the power of 10 that moves the decimal point the number of spots in the repeating portion of the decimal (in this case 100).
100 n = 3515.151515,,,
n = 35.151515...
Subtract 2nd equation from the 1st:
99 n = 3480 (notice that the decimal portions of those numbers "disappears")
Now divide by the coefficient of n.
n = 3480/99 = 1160/33 (since numerator and denominator are both divisible by 3)
Visit this Desmos graph to see that 1160/33 is equivalent to 35.1515...
desmos.com/calculator/atyujfp7in
Or just enter 1160/33 on your calculator.
Doug C.
FYI, it is a bit more complicated if the repeating portion of the decimal does not start right after the decimal point. For example: 2.13587587,,, 100N = 213.587587,,, 100000n = 213587.587587... Now when you subtract: 99900N = 213374 and so on...11/03/23